Dioptre
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A dioptre, or diopter, is a non-SI unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres (i.e. 1/metres). For example, a 3 dioptre lens brings parallel rays of light to focus at 1/3 metre.
Quantifying a lens in terms of its optical power rather than its focal length is useful because when relatively thin lenses are placed close together their powers approximately add. Thus a thin 2 dioptre lens placed close to a thin 0.5 dioptre lens yields almost the same focal length as a 2.5 dioptre lens would have. This approximation enables an optometrist to prescribe corrective lenses as a simple correction to the eye's optical power, rather than doing a detailed analysis of the entire optical system (the eye and the lens).
Since optical power is approximately additive, it can also be used to adjust a basic prescription for reading, e.g. an optometrist, having determined that a myopic person requires a basic correction of, say, -2 dioptres to restore normal distance vision, might then make a further prescription of 'add 1' for reading, to make up for lack of accommodation (ability to alter focus). This is the same as saying that +1 dioptre lenses are prescribed for reading.
The power of the eye's lens and cornea together is very high, about 40 dioptres, and the normal accommodation range of a young person is a further 15 to 20 dioptres. Most of the power comes from the curvature of the front face of the cornea, while the accommodation derives from the soft internal lens being squashed by muscles. As we get older, accommodation reduces, to about 10 dioptres at age 25 and around 1 dioptre or less at 50 and over, hence the almost universal need for older people to use reading glasses.
Convex lenses have positive dioptric value and are generally used to correct hyperopia (farsightedness) or to allow people with the limited accommodation of advancing age presbyopia to read at close range. Concave lenses have negative dioptric value and generally correct myopia (nearsightedness). Typical glasses for moderate myopia will have a power of -1.00 to -3.00 dioptres, while over the counter reading glasses will be rated at +1.00 to +3.00 dioptres. Optometrists usually measure refractive error using lenses graded in steps of 0.25 dioptres.
The dioptre can also be used as a measurement of curvature equal to the reciprocal of the radius measured in metres. For example, a circle with a radius of 1/2 metre has a curvature of 2 dioptres. If the curvature of a surface of a lens is C and the index of refraction is n, the focusing power is ɸ=(n-1)C. If both surfaces of the lens are curved, consider their curvatures as positive toward the lens and add them. This will give approximately the right result, as long as the thickness of the lens is much less than the radius of curvature of one of the surfaces. For a mirror the focusing power is ɸ=2C.
See also
es:Dioptrio fr:Dioptre he:דיופטר it:Diottria lt:Dioptrija nl:Dioptrie ja:ディオプトリ pl:Dioptria pt:Dioptria ru:Диоптрия sv:Dioptri zh:屈光度